The distance between two notes
Two notes played together, or one after another, have a measurable gap between them — that gap is an interval, and it is the single unit everything else in theory is built from. A scale is a specific sequence of intervals in a row. A chord is a specific stack of intervals on top of each other. Nothing about either is arbitrary once the intervals inside it are visible.
That single unit works whether the two notes sound at the same time — a harmonic interval, the kind heard inside a chord — or one after another — a melodic interval, the kind heard as a melody moves from note to note. Both are measured exactly the same way; only whether the notes overlap in time changes what to call the interval, not how to name it.
Naming by number: counting letter names
The numeric half of an interval’s name comes from counting letter names inclusively from the bottom note to the top. C to C is a unison, counted as one. C to D is a second. C to E is a third. Continue up to the next C and that is an octave, the eighth letter-name counted inclusively. This half of the name only cares about letter names, not exact distance — C to E and C to E♭ are both “a third,” even though they are not the same number of semitones apart, which is exactly why the number alone is never the whole name.
Counting inclusively is the detail that trips people up first: C to D is a second, not a “one-step gap,” because the count includes both the starting note and the ending note, not the distance between them the way a ruler would measure it. That’s a labelling convention, not a reflection of anything physical about the notes themselves — worth knowing explicitly rather than re-deriving it by trial and error every time.
Naming by quality: exact semitones
Quality is what pins the number down to an exact distance in semitones. Unisons, fourths, fifths and octaves are called perfect intervals because they stay a fixed, stable distance whether the surrounding key is major or minor. The rest — seconds, thirds, sixths and sevenths — come in major and minor pairs exactly one semitone apart, with major always the wider of the two: a major third spans four semitones, a minor third three. A perfect fifth spans seven semitones, the exact distance the circle of fifths is built from, stacked over and over.
Laid out from unison upward, a major scale’s own intervals from its starting note are the easiest reference: a major second at two semitones, a major third at four, a perfect fourth at five, a perfect fifth at seven, a major sixth at nine, a major seventh at eleven, and the octave at twelve — the exact same twelve-semitone arithmetic the scales-and-keys page already uses to build the scale itself, just relabelled here as distances from the starting note rather than steps between neighbours.
Push an interval a semitone beyond its major or perfect size and it becomes augmented. Pull one a semitone short of its minor or perfect size and it becomes diminished — the same twelve-semitone arithmetic this site’s scale and mode pages already use, applied to the gap between just two notes instead of a whole scale.
A handful worth knowing by ear
A short, deliberately small starting set beats trying to internalise all twelve intervals from a standing start.
- The perfect fifth — stable, almost hollow-sounding, the same interval the circle of fifths stacks repeatedly.
- The major third — bright, the sound sitting inside every major chord.
- The minor third — its darker twin, sitting inside every minor chord instead.
- The octave — the same note doubled, usually the easiest of all to hear once you know what to listen for.
Many ear-training guides pair each interval with the opening two notes of a familiar tune as a memory anchor — a perfect fourth is famously the opening leap of “Here Comes the Bride,” a major second the first two notes of “Happy Birthday” — a trick worth borrowing rather than reinventing. Once these four feel automatic, expanding to the remaining intervals — seconds, sixths, sevenths and the rest — goes considerably faster, because the ear is no longer learning the skill of interval recognition itself, only adding more entries to a method that already works.
Past the octave: compound intervals
The “Naming by number” section above stops counting at the octave — “Continue up to the next C and that is an octave… the eighth letter-name counted inclusively” — which is exactly where a second, less obvious layer of the same system picks up. Per teoria.com’s reference on the subject, “Simple intervals are not greater than an octave, while compound intervals are greater than an octave” — a ninth, tenth, eleventh or thirteenth is simply what’s left once the count keeps going past eight.
The arithmetic for naming one is direct rather than a fresh system to learn: “If you subtract 7 from a compound interval, you get the corresponding simple interval. For example, 9 - 7 = 2, so a ninth is related to a second” — and, per the same source, “a compound interval has the same quality as the simple interval to which it is related,” so a major ninth is, underneath the octave-plus wrapping, still built from the identical major-second relationship this page’s own “Naming by quality” section already defines.
Why this matters beyond just naming a wider gap
This is the same number-plus-quality system the “Why this is the piece underneath everything else” section above already says a scale, chord and progression all reduce to — compound intervals are what that system looks like once a chord voicing or a melodic leap spreads out past a single octave, which happens constantly in real playing even though the four intervals this page recommends starting with (fifth, major third, minor third, octave) all comfortably fit inside one.
It’s also the direct route to a term this site’s own chord-and-scale reference chart doesn’t use but implies: a “ninth chord” or an “eleventh chord” is named for exactly this — a compound interval stacked above the root, related back to the second or fourth degree already inside the reference chart’s own diatonic pattern, just voiced an octave higher than the plain triad shows it.
Why this is the piece underneath everything else
Once intervals are visible by name, a scale stops being a memorised list of notes and becomes a specific interval pattern that simply happens to start wherever it’s placed. A chord stops being a shape on a page and becomes a stack of thirds. A chord progression’s Roman-numeral qualities fall directly out of exactly which intervals a scale hands over at each degree. Intervals sit underneath all three, which is also why they’re the natural stop right before ear training, where the goal is recognising these same distances by ear alone, with nothing written down to check against.
It’s a genuinely small piece of vocabulary carrying a disproportionate amount of theory’s weight — number plus quality, two facts about a gap between two notes — and nearly everything on this site’s theory pages, from why a scale has the shape it has to why a chord progression’s qualities never vary within a key, ultimately reduces to that same pair of facts, repeated at different scales.
Where this comes from
teoria.com, “Reference: compound and simple intervals”. teoria.com · accessed 11 August 2026.
Common questions
What’s the difference between a major and minor third?
One semitone. A major third is four semitones wide and sounds bright; a minor third is three semitones wide and sounds darker — the difference that separates a major chord from a minor one.
Why are some intervals called “perfect”?
Unisons, fourths, fifths and octaves keep the same basic character in both major and minor keys, unlike seconds, thirds, sixths and sevenths, which shift between a major and minor version depending on the key.
Do I need to know intervals to play, or just to understand theory?
Both, eventually — intervals explain why scales and chords are built the way they are, and recognising them by ear is also the direct route into ear training and better improvising.